Elevation of Boiling Point

A liquid boils when its vapour pressure equals the external (atmospheric) pressure. For an ideal solution, Raoult's Law states that the vapour pressure of the solvent above the solution is $P_{solution} = X_{solvent} \cdot P^*_{solvent}$, where $X_{solvent}$ is the mole fraction of the solvent and $P^*_{solvent}$ is the vapour pressure of the pure solvent. Because $X_{solvent} < 1$ in any solution, $P_{solution} < P^*_{solvent}$: the vapour pressure is lowered.

Since the vapour pressure of the solution is lower than that of the pure solvent at the same temperature, the solution does not boil at the normal boiling point. The temperature must be raised until the vapour pressure of the solvent in the solution once again equals atmospheric pressure. This new, higher boiling point defines the elevation $\Delta T_b$.

The boiling point elevation is proportional to the molality of solute particles (not the molarity). Molality $m$ is defined as moles of solute per kilogram of solvent: $m = \dfrac{n_{solute}}{m_{solvent(kg)}}$. Molality is preferred over molarity because it is temperature-independent — it does not change as the solution expands or contracts with temperature fluctuations.

For electrolytes that dissociate into ions, the effective number of particles is greater than the number of formula units dissolved. The van't Hoff factor $i$ accounts for this: $i = 1$ for non-electrolytes, $i = 2$ for fully dissociated 1:1 electrolytes like $\ce{NaCl}$ (which gives $\ce{Na^+}$ and $\ce{Cl^-}$), and $i = 3$ for $\ce{CaCl_2}$ (giving $\ce{Ca^{2+}}$ and $2\,\ce{Cl^-}$). The formula $\Delta T_b = i \cdot K_b \cdot m$ incorporates this factor.

The ebullioscopic constant $K_b$ (from the Latin 'ebullire', to boil) is a solvent-specific constant with units of $\text{K}\,\cdot\,\text{kg}\,\cdot\,\text{mol}^{-1}$ (or equivalently $°\text{C}\,\cdot\,\text{kg}\,\cdot\,\text{mol}^{-1}$). For water, $K_b = 0.512\,\text{K}\,\cdot\,\text{kg}\,\cdot\,\text{mol}^{-1}$. For benzene, $K_b = 2.53\,\text{K}\,\cdot\,\text{kg}\,\cdot\,\text{mol}^{-1}$. It can be derived thermodynamically from the enthalpy of vaporisation: $K_b = \dfrac{R T_b^2 M_{solvent}}{1000\,\Delta H_{vap}}$, where $T_b$ is the normal boiling point in Kelvin and $M_{solvent}$ is the molar mass of the solvent in g/mol.

• \Delta T_b — Boiling point elevation (K or °C): The increase in boiling point of the solution compared to the pure solvent. Always positive for a dissolved solute.
• i — van't Hoff factor (dimensionless): The number of particles (ions or molecules) produced per formula unit of solute upon dissolution. $i=1$ for glucose, $i=2$ for $\ce{NaCl}$, $i=3$ for $\ce{CaCl_2}$.
• K_b — Ebullioscopic constant (K·kg·mol⁻¹): A solvent-specific constant that reflects how strongly the solvent's boiling point responds to dissolved particles. For water: $K_b = 0.512\,\text{K}\,\cdot\,\text{kg}\,\cdot\,\text{mol}^{-1}$.
• m — Molality (mol·kg⁻¹): Moles of solute dissolved per kilogram of solvent. Not to be confused with molarity (mol per litre of solution).

Problem. A student dissolves 9.00 g of glucose ($\ce{C_6H_{12}O_6}$, molar mass = 180.16 g/mol) in 250.0 g of water. What is the boiling point of this solution? ($K_b$ for water = 0.512 K·kg·mol⁻¹; normal boiling point of water = 100.00 °C; glucose does not dissociate, so $i = 1$.)

Answer. The boiling point of the glucose solution is approximately 100.10 °C.

• Depression of Freezing Point — Freezing point depression is a closely parallel colligative property; both use the same molality-based formula structure with a cryoscopic constant (K_f) instead of K_b, making the two concepts natural companions.
• Raoult's Law and Vapour Pressure Lowering — Boiling point elevation is mechanistically caused by vapour pressure lowering described by Raoult's Law. Understanding the vapour pressure relationship is essential to explaining why the boiling point rises.
• Osmotic Pressure — Osmotic pressure is another colligative property that depends on the concentration of solute particles, illustrating the broader principle that solute presence affects multiple physical properties of solutions.
• Molality and Solution Concentration — Molality is the specific concentration unit used in all colligative property calculations, and a solid understanding of how to calculate it is a prerequisite for applying the boiling point elevation formula correctly.
• van't Hoff Factor and Electrolyte Dissociation — The van't Hoff factor i modifies the boiling point elevation formula for ionic compounds. Understanding ionic dissociation of electrolytes like NaCl and CaCl₂ is critical to accurately calculating ΔT_b for real solutions.